<html><body>
<h1>DTF result window</h1>

<p>This window presents results from DTF (Directed Transfer Function)
method. The method is formulated in the framework of AR model.
Elements of the transfer function matrix for multichannel EEG process,
properly normalized, appear to be good estimators of the propagation
direction and spectral properties of the investigated signals.</p>

<p>Model coefficients are estimated from the input signal
using the Yule-Walker method. Prior to coefficient estimation,
all input channels are independently normalized to mean=0 and variance=1.</p>

<h2>Model order</h2>
<p>The main graph presents values of several criteria facilitating
selection of most suitable model order. The analytical formulae of the
criteria can be displayed by hovering mouse on the label in the legend area.
Variables in formulae describe as follows:</p>
<ul>
	<li>channels: number of selected channels from the input signal</li>
	<li>order: AR model order > 0</li>
	<li>samples: number of samples in the selected signal</li>
	<li>V: covariance matrix of the residual noise, its dimensions are: channels × channels</li>
</ul>
<p>The best model order correspond to the lowest value of the criterion.
After selecting preferred model order by clicking on the graph,
data of the chosen AR model will be displayed in the other sections
of the window: <em>Transfer functions</em> and <em>Transfer graph</em>.</p>

<p>Also, it is possible to copy coefficients of the selected model to
the clipboard. The data will be aligned as 3-dimensional array
(list of coefficient matrices), ordered by the ascending time lag:
1, 2, 3, (…) up to model order. For example, for a order-2 single-channel model described as
x(t) = 0.8061560601208944 x(t−1) − 0.2625742978704753 x(t−2) + ε(t)
the output is
<pre>[[[0.8061560601208944]],[[-0.2625742978704753]]]</pre>
while for an order-2 multi-channel model (three channels) the output would be presented as
<pre>[[[0.8061065403359177,0.016318446822562428,-0.061749715159001295],[0.236878938920024,0.39264247253218987,0.005563227997886028],[0.07746866368897523,0.052281999563032054,0.20082386391939483]],[[-0.20869955649173783,-0.0023608446650237773,0.050938878243404005],[-0.05294976129376853,-0.4927536408857016,0.021964746581938435],[-0.22203468218993755,0.01008725282993888,-0.6093122774503732]]]</pre>
</p>

<h2>Transfer functions</h2>
<p>The top switch allows to select whether normalized or unnormalized DTF
should be calculated. Normalization is applied in such a way, that for every
frequency and every source channel, sum of the transfer values to all channels
(including the self-transfer) is equal to 1.</p>

<p>The diagonal plots represent spectra of channels, regardless of
the normalization selection described above. Non-diagonal entries
represent values of the transfer functions (normalized or not)
between different channels.</p>

<h2>Transfer graph</h2>
<p>Transfer graph represent values of the transfer function
averaged over specified frequency interval. The relative intensity of
the transfer is represented by colour (from blue to red) and opacity
(from transparent to opaque) of arrows between the labeled circles
representing selected channels of the input signal.</p>

<h2>Literature</h2>
<ol>
<li>Kamiński M. J., Blinowska K. J.:
A new method of the description of the information flow in the brain structures,
<em>Biological Cybernetics</em> July 1991, Volume 65, Issue 3, pp 203-210</li>
</ol>

</body></html>
